In this study, an experimental investigation was conducted to determine the triaxial tensile-compressive-compressive (T–C–C) behavior of three different high-performance concrete (HPC) groups with uniaxial compressive strength ranging from 44 to 90 MPa, using servo-hydraulic actuators. In the experimental program, seventeen stress ratios for each batch of HPC were designed, ultimate strength, principal stress–strain curves under T–C–C were measured and recorded, as well as crack patterns. The test results revealed that the uniaxial compressive strength and the stress ratios had a negative effect on the normalized ultimate strength and deformation of HPCs under T–C–C loading. An increase in the minimum principal stress (tensile stress) significantly decreased the ultimate strength, stiffness, and ductility of the HPC samples. Compared with the minimum principal stress effect, intermediate principal stress effect is not obvious for HPCs at different stress ratios. With increasing uniaxial compressive strength, the obtained normalized ultimate strength and deformability of HPCs decrease. Tensile brittle failure mode was observed for the HPC samples under triaxial T–C–C loading. Finally, a modified four-parameter failure criterion was established for HPC based on the experimental results, regarding the effect of uniaxial compressive strength.